Algebra - I
Offered By: IMSC via Swayam
Course Description
Overview
Foundational PG level course in algebra, suitable for M.Sc and first year PhD students in Mathematics.INTENDED AUDIENCE :Any Interested LearnersPREREQUISITES :BSc-level linear algebraINDUSTRIES SUPPORT :Not Applicable
Syllabus
Week 1:Permutation Groups, symmetries of graphsWeek 2:Abstract Groups, homomorphism, isomorphism, subgroup, quotient groupWeek 3:Group actionsWeek 4:Sylow theorems
Week 5:Examples and definition of ringsWeek 6:Homomorphisms, ideals, quotients, integral domains, fraction fieldsWeek 7:Principal ideal domains, Unique factorization domains and Euclidean domainsWeek 8:Modules, definition and examples, submodules, simplicity, indecomposability
Week 9:Tensor productsWeek 10:Jordan-Holder and Krull-Schmidt theoremsWeek 11:Classification of finitely generated modules over PID’sWeek 12:Applications of classification to finitely generated abelian groups and Jordan canonical form
Week 5:Examples and definition of ringsWeek 6:Homomorphisms, ideals, quotients, integral domains, fraction fieldsWeek 7:Principal ideal domains, Unique factorization domains and Euclidean domainsWeek 8:Modules, definition and examples, submodules, simplicity, indecomposability
Week 9:Tensor productsWeek 10:Jordan-Holder and Krull-Schmidt theoremsWeek 11:Classification of finitely generated modules over PID’sWeek 12:Applications of classification to finitely generated abelian groups and Jordan canonical form
Taught by
Prof. S. Viswanath, Prof. Amritanshu Prasad
Related Courses
Intermediate AlgebraUniversity of California, Irvine via Coursera Algebra & Algorithms
Moscow Institute of Physics and Technology via Coursera Algebra and Differential Calculus for Data Science
University of Colorado Boulder via Coursera Álgebra básica
Universidad Nacional Autónoma de México via Coursera College Algebra
Doane University via edX